• Join over 1.2 million students every month
  • Accelerate your learning by 29%
  • Unlimited access from just £6.99 per month

Analysis of Bivariate Data - I aim to investigate the relationship between score in the P1 mock paper and score in the P1 exam. My population is lower sixth students at Peter Symonds College.

Extracts from this document...


Aidan Russell-Gear                Page  of

S2 Coursework – Analysis of Bivariate Data


        I aim to investigate the relationship between score in the P1 mock paper and score in the P1 exam. My population is lower sixth students at Peter Symonds College; I have obtained a table of 304 students which tells me their maths A-level course, gender, average GCSE score, results in P1 tests 1 and 2, P1 mock and P1 exam, from the college maths department.

        I wish to investigate this relationship so that my results may be used in the future by teachers and students to assess whether it is fair to base a prediction of the likely P1 exam score on the P1 mock result. I hope this will prove useful in deciding future options and motivating students to self-improvement. I hope then to prove convincingly whether the P1 exam result is correlated with the P1 mock result, and to what extent is this correlation.

        From my population of 304 students I took a sample of 50 to analyse for ease of calculation, I obtained this group by a simple random sample method. I assigned a random number to each student, then sorted the data in descending order and took the first 50 students as my sample.

...read more.


Pearson’s product moment correlation coefficient:

        And so the value of r was found to be 0.798922, and we see this result is a strong indication of positive correlation. However, this is merely my informed opinion, in order to get a more definitive answer to whether these two variables are correlated we must perform a hypothesis test.

Hypothesis Test

        To do this I must use the tables of critical values found in the MEI student handbook. These are standard pre-calculated values which will indicate whether or not my data are correlated, again assuming random normal distribution.

        My starting hypothesis, the null hypothesis (H0), is that there is no correlation between the P1 mock and P1 result in the population at all, my second (H1) is that there is some positive correlation. It is clear that there is no negative correlation and so I can merely look at the probabilities of positive correlation. I will perform a hypothesis test against the correlation coefficient of the parent population, ρ, my value of r is an estimate to ρ taken from a sample of the parent population.

                H0:        ρ = 0

                H1:        ρ > 0

...read more.


Note that my population was only from one year at Peter Symonds College and students could vary from year to year, though this is unlikely to be significant. However when performing the hypothesis test I assumed that my correlation coefficient was a good estimate for ρ, the parent correlation coefficient, and this was central to the validity of the hypothesis testing as a method of analysis. I feel that this is acceptable due to the high nature of the calculated correlation coefficient compared to the critical values for ρ calculated at 5% and at 0.5%, thus I feel that any error can be accommodated by the significantly larger value of the calculated coefficient than the critical value. This difference is so large that I am convinced of the validity of the relationship.


        The following sources were used in my in my investigation:

MEI Structured Mathematics – Statistics 2 (second edition)

MEI Structured Mathematics – Students’ Handbook

...read more.

This student written piece of work is one of many that can be found in our AS and A Level Probability & Statistics section.

Found what you're looking for?

  • Start learning 29% faster today
  • 150,000+ documents available
  • Just £6.99 a month

Not the one? Search for your essay title...
  • Join over 1.2 million students every month
  • Accelerate your learning by 29%
  • Unlimited access from just £6.99 per month

See related essaysSee related essays

Related AS and A Level Probability & Statistics essays

  1. Data Handling - Planning - I intend to investigate the relationship between the number ...

    This is known as the interquartile range. Interquartile range = upper quartile - lower quartile Interquartile range is an important measure of spread. It shows how widely the data is spread. If the interquartile range is small, the middle half of the distribution is bunched together.

  2. GCSE Mathematics Coursework: Statistics Project

    weight, five of the six boys who watch the largest amount of television in the sample, are below the average weight or just slightly over. Fig 4 shows a stronger negative correlation than Fig 3 (as the r value is -0.13)

  1. Intermediate Maths Driving Test Coursework

    I think Instructor C however is better than A or B so far in teaching both male and female as they both had the lowest mistakes. From this graph we can see a fairly strong negative correlation however it is a gentle slope of a line ad very high up despite high amount of lessons.

  2. The aim of this investigation was to look at the reliability and validity of ...

    For a trait theory to be acceptable as a personality theory it must firstly isolate basic traits which describe personality and measure them accurately. This is attempted using a process called Factor Analysis. A pioneer in this field was Raymond Cattell (1965).

  1. Statistics. The purpose of this coursework is to investigate the comparative relationships between the ...

    low income). If their lifestyle is abruptly changed, they may consider selling their car for a less/ more expensive model. The car will be passed on during this to people in similar financial lifestyles that the owner had originally. When the vehicle is passed on, essential parts will become to be more reliable.

  2. Anthropometric Data

    I will able to draw my line of best fit this will be drawn visually and also able to find the correlation coefficient in this case the value of r. Prediction 2 Looking at the scatter graph I can visually predict that I will get a fairly fat ellipse has the points are quite spread out has.

  1. Fantasy Football - Maths Coursework - Statistics

    and 7+ ratings affecting the number of points more than Clean Sheets and Goals scored in Hypothesis 2. If I were to pick a fantasy football team based on my findings then I would make sure that I picked defenders because they are more consistent at scoring well.

  2. Guestimate - investigate how well people estimate the length of lines and the size ...

    Frequency Class width Freq. Density 0 < d < 20 1 20 0.05 20 < d < 30 0 10 0 30 < d < 35 4 5 0.8 35 < d < 45 4 10 0.4 45 < d < 55 12 10 1.2 55 < d < 70

  • Over 160,000 pieces
    of student written work
  • Annotated by
    experienced teachers
  • Ideas and feedback to
    improve your own work